In a △ABC if cos⁡Acos⁡Bcos⁡C=3−18 and sin⁡Asin⁡Bsin⁡C=3+38, thenThe value of tan A + tan B + tan C is The value of tan A tan B + tan B tan C + tan C tan A isThe respective values of tan A ,tan B and tan C are

∴cos⁡Acos⁡Bcos⁡C=3−18sin⁡Asin⁡Bsin⁡C=3+38∴tan⁡Atan⁡Btan⁡C=3+33−1....(1)Now tanA + tan B + tanC = tanA tanB tanC=3+33−1....(2)Now A+B+C=π∴cos⁡(A+B+C)=−1∴cos⁡Acos⁡Bcos⁡C[1−Σtan⁡Atan⁡B]=−1∴3−18[1−Σtan⁡Atan⁡B]=−1⇒Σtan⁡Atan⁡B=5+43.....(3)From (1), (2) and (3), we gettan A, tan B, tan C are roots ofx3−3+33−1x2+(5+43)x−(3+3)3−1=0or x3−(2+3)3x2+(5+43)x−(2+3)3=0or  x3−(3+23)x2+(5+43)x−(3+23)=0or (x−1)(x−3)(x−(2+3))=0∴    tan⁡A=1,tan⁡B=3,tan⁡C=2+3